In a circle with a radius of 7.5 cm, the diameter of the AC and the chord of the AK is 9 cm, find the length of the chord CK.

The chords AK and СK form an angle AKС inscribed in the circle, which rests on the arc AC.
Since the segment AC is the diameter of the circle, the arc AC = 1800, and then the inscribed angle AKС = 180/2 = 90.
Then the triangle AKC is rectangular, in which the hypotenuse AC is the diameter of the circle.
AC = 2 * R = 2 * 7.5 = 15 cm.
By the Pythagorean theorem, in the right-angled triangle AKС, we determine the length of the leg CК.
CK ^ 2 = AC ^ 2 – AK ^ 2 = 225 – 81 = 144.
СK = 12 cm.
Answer: The length of the chord СК is 12 cm.